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Fractional Order Systems and Their Applications

Fractional calculus (FC) generalizes the concepts of derivative and integral orders to non-integer orders. It was introduced by Leibniz (1646–1716) but remained a purely mathematical exercise for a long time, despite the original contributions to the field of important mathematicians, physicists, an...

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Format: Online
Sprog:engelsk
Udgivet: MDPI - Multidisciplinary Digital Publishing Institute 2025
Fag:
Parrodo’paradox
Mann iteration
Julia set
alternated system
connectivity
fuzzy fractional differential equations
Caputo derivative
fractional hyperbolic function
strongly generalized Hukuhara differentiability
Ulam-type stability
Hermite–Hadamard inequality
exponentially nonconvex function
modified Fox–Wright function
fractional integrals
error estimation
Leslie–Gower
double Allee effect
Hopf bifurcation
global stability
nonlocal operator
Kalman filter
state of charge
fuzzy inference
lithium-ion batteries
Maglev system
fractional order PID
fractional order sliding mode
fractional order fuzzy control
GWO-PSO
Liu process
Caputo fuzzy fractional differential equations
fuzzy process
credibility space
inverse problem
spectral collocation method
fractional diffusion
fractional calculus
fractional-order
digital manufacturing
supply chain
synchronization
control
fractional-order system
multi-agent
guaranteed cost consensus
delay-dependent
ψ-Hilfer fractional derivative
Riemann–Liouville fractional derivative
Caputo fractional derivative
system of fractional differential equations
fractional-order Jerk system
chaos
hopf bifurcation
stability
time delay feedback controller
fractional-order PDσ controller
delayed linear fractional-order systems
feedback controller
positive invariant set
asymptotic stabilization
n/a
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
Online adgang:ONIX_20250220_9783725826803_386
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Summary:Fractional calculus (FC) generalizes the concepts of derivative and integral orders to non-integer orders. It was introduced by Leibniz (1646–1716) but remained a purely mathematical exercise for a long time, despite the original contributions to the field of important mathematicians, physicists, and engineers. FC has experienced rapid development in recent decades, both in mathematics and applied sciences, being recognized as an excellent tool to describe complex dynamics. Based on this, several models governing physical phenomena in the areas of science and engineering have been reformulated in light of FC for them to better reflecting their non-local and frequency- and history-dependent properties. Applications of FC include modeling of diffusion, viscoelasticity, and relaxation processes in fluid mechanics; the dynamics of mechanical, electronic, and biological systems; and signal processing and control. This reprint compiles articles from the Special Issue “Fractional Order Systems and Their Applications”, which focused on original and new research results on modeling and control of fractional order systems with applications in science and engineering. It includes 13 manuscripts addressing novel issues and specific topics that illustrate the richness and applicability of fractional calculus.

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